Such an insulating device is disclosed in European patent EP 1 134 478 B1 for a machine element configured as an exhaust gas pipe through which a hot medium, namely, the exhaust gas, can flow, said machine element belonging to an aggregate configured as an internal combustion engine. The insulating device includes an inner jacket that surrounds the machine element or the exhaust gas pipe, as well as an outer jacket arranged at a distance from the inner jacket, whereby there is a cavity between these jackets that is filled with replaceable insulating material. The inner jacket and the outer jacket are configured in such a flexible manner that they can be slipped over the machine element or exhaust gas pipe in that their ends are spread apart and subsequently, they can be attached by means of a fastener configured, for example in the form of one or more straps, directly to the machine element that is joined to the aggregate in a known manner. This insulating device has proven its worth for many application cases, but in other applications, special requirements mean that there is a considerable need for solutions of a different nature. For instance, assembly as well as inspection or repair procedures involve a substantial amount of work when it comes to affixing or releasing the fastener and/or the screwed connections that serve to join additional components. If the above-mentioned first machine element is connected to at least one additional machine element, especially to an exhaust gas manifold, then this element is not adequately insulated by the prior-art insulating device.